Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 13 x + 87 x^{2} - 299 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.207871921947$, $\pm0.310374946937$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.53525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $5$ |
Isomorphism classes: | 5 |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $305$ | $283345$ | $151716455$ | $78782660525$ | $41453629822000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $11$ | $535$ | $12467$ | $281523$ | $6440556$ | $148031155$ | $3404741897$ | $78310681203$ | $1801152333461$ | $41426510927550$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+5x^5+11x^4+16x^2+2x+2$
- $y^2=19x^6+12x^5+2x^4+14x^3+5x^2+8x+19$
- $y^2=7x^6+16x^5+6x^4+10x^3+16x^2+x+13$
- $y^2=5x^6+16x^5+18x^4+4x^3+21x^2+3x+19$
- $y^2=10x^6+17x^5+x^4+14x^3+11x^2+16x+22$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The endomorphism algebra of this simple isogeny class is 4.0.53525.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
2.23.n_dj | $2$ | (not in LMFDB) |